Solution
The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four- line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
[tex]a\times b=c\times d[/tex][tex]\begin{gathered} (4x+2)8=9(4x) \\ \end{gathered}[/tex]
Open the bracket
[tex]\begin{gathered} (4x+2)8=9(4x) \\ 32x+16=36x \\ \text{collect the like terms} \\ 16=36x-32x \\ 16=4x \\ \text{Divide both sides by 4} \\ \frac{16}{4}=\frac{4x}{4} \\ \\ x=4 \end{gathered}[/tex]
